Here \(\epsilon ^{a}\)  is a unit polarization vector possessing the spacetime index \(a\)  \((a=0,1,2,3)\) 
which is the same as the spin index and is needed to incorporate minimally the spin DOF for the massive photon with spin one. Here we have
considered the Lorentz frame where \(\epsilon ^{a}\)  is purely space-like so that we can readily find
\(\epsilon ^{a}\epsilon ^{a}=\vec{\epsilon }\cdot \vec{\epsilon }=1\) , or
\(\epsilon _{a}\epsilon ^{a}=-\vec{\epsilon }\cdot \vec{\epsilon }=-1\)  with \(\vec{\epsilon }=(\epsilon ^{1},\epsilon ^{2},\epsilon ^{3})^{t}\) . Moreover
we have the relation \(\epsilon _{a}p^{a}\ne 0\) , since for the massive photon we have longitudinal component in addition to transverse ones,
similar to a phonon case. For more details about the phonon polarization, see Ref. [1]} for instance.
Next we have the normalization relations: \(\bar{u}^{a}u^{a}\equiv u^{a\dagger }\sigma _{3}u^{a}=1\) ,
\(u^{a~\dagger }u^{a}=\frac{E}{m}\) , \(\bar{v}^{a}v^{a}\equiv v^{a\dagger }\sigma _{3}v^{a}=-1\)  and \(v^{a~\dagger }v^{a}=\frac{|E|}{m}\) .
It is well known that, in the Dirac RQM for the positron, we have the electron and positron corresponding to the positive and negative energy solutions, respectively. It is now interesting to note that, similar to the Dirac theory for the positron, in the universe
there exist the photon with positive energy solution and the antimass-photon with negative energy solution,
if we assume that the relativistic spin one photon possesses mass.
